Jun Zhu
Publications
Why the Maximum Second Derivative of Activations Matters for Adversarial Robustness
This work investigates the critical role of activation function curvature -- quantified by the maximum second derivative $\max|σ''|$ -- in adversarial robustness. Using the Recursive Curvature-Tunable Activation Family (RCT-AF), which enables precise control over curvature through parameters $α$ and $β$, we systematically analyze this relationship. Our study reveals a fundamental trade-off: insufficient curvature limits model expressivity, while excessive curvature amplifies the normalized Hessian diagonal norm of the loss, leading to sharper minima that hinder robust generalization. This results in a non-monotonic relationship where optimal adversarial robustness consistently occurs when $\max|σ''|$ falls within 4 to 10, a finding that holds across diverse network architectures, datasets, and adversarial training methods. We provide theoretical insights into how activation curvature affects the diagonal elements of the hessian matrix of the loss, and experimentally demonstrate that the normalized Hessian diagonal norm exhibits a U-shaped dependence on $\max|σ''|$, with its minimum within the optimal robustness range, thereby validating the proposed mechanism.
RDT2: Exploring the Scaling Limit of UMI Data Towards Zero-Shot Cross-Embodiment Generalization
Vision-Language-Action (VLA) models hold promise for generalist robotics but currently struggle with data scarcity, architectural inefficiencies, and the inability to generalize across different hardware platforms. We introduce RDT2, a robotic foundation model built upon a 7B parameter VLM designed to enable zero-shot deployment on novel embodiments for open-vocabulary tasks. To achieve this, we collected one of the largest open-source robotic datasets--over 10,000 hours of demonstrations in diverse families--using an enhanced, embodiment-agnostic Universal Manipulation Interface (UMI). Our approach employs a novel three-stage training recipe that aligns discrete linguistic knowledge with continuous control via Residual Vector Quantization (RVQ), flow-matching, and distillation for real-time inference. Consequently, RDT2 becomes one of the first models that simultaneously zero-shot generalizes to unseen objects, scenes, instructions, and even robotic platforms. Besides, it outperforms state-of-the-art baselines in dexterous, long-horizon, and dynamic downstream tasks like playing table tennis. See https://rdt-robotics.github.io/rdt2/ for more information.